Compatibility of Cyclic Causal Structures with Spacetime in General
Theories with Free Interventions
- URL: http://arxiv.org/abs/2211.03593v3
- Date: Mon, 24 Apr 2023 20:14:33 GMT
- Title: Compatibility of Cyclic Causal Structures with Spacetime in General
Theories with Free Interventions
- Authors: Maarten Grothus
- Abstract summary: We show the possibility of operationally detectable causal loops embedded in (1+1)-Minkowski spacetime without superluminal signalling.
We establish new properties of HO affects relations and apply them to infer causal structures.
We study the embedding of information-theoretic causal structures into partially ordered spacetimes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: By relating and ordering events, causality constitutes a pivotal feature of
our world. On the one hand, there are information-theoretic notions of
causality defined in terms of the information processing ability of agents and
on the other hand, there are relativistic notions of causality tied to a
spacetime. In this thesis, we improve upon a framework introduced by V.
Vilasini and R. Colbeck in PRA, 106, 032204 (2022) and PRL, 129, 110401 (2022)
for connecting these notions, where the possibility of operationally detectable
causal loops embedded in (1+1)-Minkowski spacetime without superluminal
signalling was demonstrated. In the first part, we take the
information-theoretic point of view, where the concept of higher-order (HO)
affects relations was proposed to generically model signalling in the presence
of cyclic, fine-tuned and non-classical causal influences. We establish new
properties of HO affects relations and apply them to infer causal structures.
We then demonstrate a complete and constructive way to detect causal loops from
a set of HO affects relations. In the second part, we study the embedding of
information-theoretic causal structures into partially ordered spacetimes. We
propose stability conditions on the spacetime embedding to rule out a class of
operationally detectable loops that cannot be ruled out by the principle of
no-signalling (outside the relativistic future) alone. We then propose novel
order-theoretic properties that we conjecture to hold in Minkowski spacetime
with $d \geq 2$ spatial dimensions. This would imply that in contrast to
(1+1)-Minkowski spacetime, in higher dimensions, the no-signalling principle is
indeed sufficient for ruling out this class of loops. Finally, we introduce a
relation which allows for causal inference through knowledge about the absence
of signalling relations and we relate it to novel order-theoretic features of
spacetime.
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